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What’s Happening in the Mathematical Sciences, Volume 6

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Dana Mackenzie; Barry Cipra

The AMS series What's Happening in the
Mathematical Sciences distills the amazingly rich brew of current
research in mathematics down to a few choice samples. This volume
leads off with an update on the Poincaré Conjecture, a
hundred-year-old problem that has apparently been solved by Grigory
Perelman of St. Petersburg, Russia. So what did topologists do when
the oldest and most famous problem about closed manifolds was
vanquished? As the second chapter describes, they confronted a suite
of problems concerning the “ends” of open
manifolds… and solved those, too.

Not to be outdone, number theorists accomplished several unexpected
feats in the first five years of the new century, from computing a
trillion digits of pi to finding arbitrarily long equally-spaced
sequences of prime numbers. Undergraduates made key discoveries, as
explained in the chapters on Venn diagrams and primality testing. In
applied mathematics, the Navier-Stokes equations of fluid mechanics
continued to stir up interest. One team proved new theorems about the
long-term evolution of vortices, while others explored the surprising
ways that insects use vortices to move around. The random jittering of
Brownian motion became a little less mysterious. Finally, an old and
trusted algorithm of computer science had its trustworthiness
explained in a novel way.

Barry Cipra explains these new developments in his wry and witty style,
familiar to readers of Volumes 1–5, and is joined in this volume by Dana
Mackenzie. Volume 6 of What's Happening will convey to all
readers—from mathematical novices to experts—the beauty and
wonder that is mathematics.

Click here to listen to
interviews with authors Barry Cipra and Dana Mackenzie.

The AMS series What's Happening in the
Mathematical Sciences distills the amazingly rich brew of current
research in mathematics down to a few choice samples. This volume
leads off with an update on the Poincaré Conjecture, a
hundred-year-old problem that has apparently been solved by Grigory
Perelman of St. Petersburg, Russia. So what did topologists do when
the oldest and most famous problem about closed manifolds was
vanquished? As the second chapter describes, they confronted a suite
of problems concerning the “ends” of open
manifolds… and solved those, too.

Not to be outdone, number theorists accomplished several unexpected
feats in the first five years of the new century, from computing a
trillion digits of pi to finding arbitrarily long equally-spaced
sequences of prime numbers. Undergraduates made key discoveries, as
explained in the chapters on Venn diagrams and primality testing. In
applied mathematics, the Navier-Stokes equations of fluid mechanics
continued to stir up interest. One team proved new theorems about the
long-term evolution of vortices, while others explored the surprising
ways that insects use vortices to move around. The random jittering of
Brownian motion became a little less mysterious. Finally, an old and
trusted algorithm of computer science had its trustworthiness
explained in a novel way.

Barry Cipra explains these new developments in his wry and witty style,
familiar to readers of Volumes 1–5, and is joined in this volume by Dana
Mackenzie. Volume 6 of What's Happening will convey to all
readers—from mathematical novices to experts—the beauty and
wonder that is mathematics.

Click here to listen to
interviews with authors Barry Cipra and Dana Mackenzie.